ASPRS Guidelines Vertical Accuracy Reporting for Lidar Data by wpk13069

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									ASPRS Guidelines
Vertical Accuracy Reporting for Lidar Data

Version          1.0
Drafted          May 15, 2004
Released         May 24, 2004
Ownership        ASPRS Lidar Committee (PAD)
Editor           Martin Flood


Scope
This document identifies the vertical accuracy reporting requirements that are recommended by
the American Society for Photogrammetry and Remote Sensing (ASPRS) when analyzing
elevation data generated using airborne light detection and ranging or laser radar (lidar)
technology. ASPRS recommends all mapping professionals adhere to and follow these
guidelines when generating mapping products derived from lidar data.


Reference Standards
These ASPRS guidelines are harmonized with the relevant sections of the Guidelines for Digital
Elevation Data (Version 1.0) released by the National Digital Elevation Program (NDEP). The
sections on vertical accuracy testing and reporting from the NDEP guidelines have been
submitted to the Federal Geographic Data Committee (FGDC) for inclusion as approved revisions
to the National Standard for Spatial Data Accuracy (NSSDA). The NDEP guidelines are
available online at www.ndep.gov. For reference, the corresponding section references from the
NDEP guidelines are cross-referenced and tabulated against section numbers in this document in
Appendix A. If cases occur where these ASPRS guidelines are found to be in conflict with the
NSSDA, the NSSDA is the controlling document and takes precedent.


Ethical Conduct and Public Health & Safety
ASPRS reminds mapping practitioners who are engaged in the use, development, and
improvement of the mapping sciences and related disciplines such as lidar, that they should abide
by the principles outlined in the ASPRS Code of Ethics, especially as it relates to the appropriate
and honest application of photogrammetry, remote sensing, geographic information systems, and
related spatial technologies. ASPRS recommends that mapping professionals always review lidar
data vertical accuracy reporting requirements in terms of the potential harm that could be done to
the public health and safety in the event that the elevation data fail to satisfy the specified vertical
accuracy.




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Guidelines

1. Accuracy Requirements

    1.1. Vertical Accuracy
    Vertical accuracy is the principal criterion in specifying the quality of elevation data, and
    vertical accuracy requirements depend upon the intended user applications.1 There are five
    principal applications where high vertical accuracy is normally required of digital elevation
    datasets:

                  (1) For marine navigation and safety.
                  (2) For storm water and floodplain management in flat terrain.
                  (3) For management of wetlands and other ecologically sensitive flat areas.
                  (4) For infrastructure management of dense urban areas where planimetric maps
                      are typically required at scales of 1 inch = 100 feet and larger scales.
                  (5) For special engineering applications where elevation data of the highest
                      accuracy are required.

    Whereas there is a tendency to specify the highest accuracy achievable for many other
    applications, users of elevation data must recognize that lesser standards may suffice,
    especially when faced with the increased costs for higher accuracy elevation data.

    When contracting for lidar-derived elevation data, it is important to specify the vertical
    accuracy expected for all final products being delivered. For example, when contours or
    gridded digital elevation models (DEMs) are specified as deliverables from lidar-generated
    mass points, a TIN may first be produced from which a DEM or contours are derived. If
    done properly, error introduced during the TIN to contour/DEM process should be minimal;
    however, some degree of error will be introduced. Accuracy should not be specified and
    tested for the TIN with the expectation that derivatives will meet the same accuracy.
    Derivatives may exhibit greater error, especially when generalization or surface smoothing
    has been applied to the final product. Specifying accuracy of the final product(s) requires the
    data producer to ensure that error is kept within necessary limits during all production steps.

    It should be noted that many states have regulations that require elevation data to be produced
    by licensed individuals to protect the public from any harm that an incompetent data producer
    may cause. Traditionally, such licensing is generally linked to experience in proving that
    products are delivered in accordance with the National Map Accuracy Standards (NMAS), or
    equivalent. Information about the National Map Accuracy Standard (NMAS) and the
    National Standard for Spatial Data Accuracy (NSSDA) is available from a variety of sources,
    including "Digital Elevation Model Technologies and Applications: The DEM Users
    Manual" and Part 5 of the referenced NDEP guidelines. An understanding of the basic
    principles of these Standards will be helpful for understanding the following guidelines for
    determining vertical accuracy requirements for lidar-derived elevation data.

    With the NSSDA, the vertical accuracy of a data set (Accuracy(z)) is defined by the root mean
    square error (RMSE(z)) of the elevation data in terms of feet or meters at ground scale, rather
    than in terms of the published map's contour interval. Because the NSSDA does not address

1
  See Chapter 11, "Digital Elevation Model Technologies and Applications: The DEM Users Manual," ASPRS, 2001
for a more detailed discussion.


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    the suitability of data for any particular product, map scale, contour interval, or other
    application, no error thresholds are established by the standard. However, it is often helpful
    to use familiar NMAS thresholds for determining reasonable NSSDA accuracy requirements
    for various types of terrain and relief. This relationship can be shown to be:

                [1] NMAS CI = 3.2898*RMSE(z)
                [2] NMAS CI = Accuracy(z)/0.5958

                where

                [3] Accuracy(z) = 1.9600*RMSE(z) (Normally Distributed Error)

    Note that for error that is not normally distributed, ASPRS recommends Accuracy(z) be
    determined by 95th percentile testing, not by the use of Equation [3]. A normal distribution
    can be tested for by calculating the skewness of the dataset. If the skew exceeds ±0.5 this is a
    strong indicator of asymmetry in the data and further investigation should be completed to
    determine the cause. Based on this relationship, the Accuracy(z) values shown in Table 1
    below are NSSDA equivalents to the NMAS error thresholds for common contour intervals
    and should be taken as the recommended ASPRS vertical accuracy requirements for lidar
    data to support mapping products that meet the corresponding NMAS standard.

           NMAS                       NSSDA                   NSSDA  Required Accuracy
      Equivalent Contour              RMSE(z)                        for Reference Data
                                                             Accuracy(z)
           Interval                                                          for
                                                                      “Tested to Meet”
               0.5            0.15 ft or 4.60 cm 0.30 ft or 9.10 cm        0.10 ft
                1             0.30 ft or 9.25 cm 0.60 ft or 18.2 cm        0.20 ft
                2             0.61 ft or 18.5 cm 1.19 ft or 36.3 cm        0.40 ft
                4             1.22 ft or 37.0 cm 2.38 ft or 72.6 cm        0.79 ft
                5             1.52 ft or 46.3 cm 2.98 ft or 90.8 cm        0.99 ft
               10             3.04 ft or 92.7 cm 5.96 ft or 181.6 cm       1.98 ft
                     Table 1 Comparison of NMAS/NSSDA Vertical Accuracy

    In contracting for lidar data production, the required vertical accuracy should be specified in
    terms of Accuracy(z), rather than NMAS CI, the correct value for which may be calculated
    from Equation [2] above for any given NMAS CI, extracted from the third column of Table 1
    or uniquely derived for a particular application. Consistent use of the User Requirements
    Menu when contracting/specifying lidar-derived elevation data is highly recommended by
    ASPRS. Details of the User Requirements Menu can be found in the NDEP Guidelines or the
    DEM Manual referenced earlier.

    However, it should be noted that stating a single vertical accuracy requirement without
    providing additional clarification and details of the intended purpose of the lidar-derived
    elevation dataset may not be sufficient information to allow for proper planning and
    implementation of the field data collection by the data provider. Testing of lidar-derived
    elevation data over various ground cover categories has revealed that the magnitude and
    distribution of errors often vary between different land cover types. To account for this,
    ASPRS recommends the following:




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        1. For ASPRS purposes, the lidar dataset’s required “fundamental” vertical accuracy,
           which is the vertical accuracy in open terrain tested to 95% confidence (normally
           distributed error), shall be specified, tested and reported. If no distinction is made
           when a document references “vertical accuracy”, it shall be assumed to be
           “fundamental” (best case) vertical accuracy.
        2. If information is required on the vertical accuracy achieved within other ground
           cover categories outside open terrain, either to meet the same specification as the
           fundamental vertical accuracy or a more relaxed specification, then “supplemental”
           vertical accuracies, that is vertical accuracy tested using the 95th percentile method
           (not necessarily normally distributed) shall be specified, tested and reported for each
           land cover class of interest.
        3. If contour maps or similar derivative products are to be generated across an entire
           project area, the project-wide vertical accuracy requirement shall be the same as
           calculated by Equation [1] or listed in Table 1 across all land cover classes. For
           ASPRS purposes this means that vertical accuracy in such cases shall be specified,
           tested and reported for each land cover class, reporting a fundamental vertical
           accuracy in open terrain and a supplemental vertical accuracy in each unique land
           cover class, each of which must independently meet the requirements for the desired
           contour interval.
        4. Contour maps or similar derivative products that cover several different land cover
           classes in a project shall only be reported as “Tested” or “Compiled to Meet” (see
           Section 3.2) a given accuracy in accordance with the worst vertical accuracy,
           fundamental or supplemental, of any of the land cover classes to be included in the
           mapping product.
        5. In some circumstances, it may be preferable to specify a different vertical accuracy in
           different land cover classes, specifying a relaxed vertical accuracy in forested areas,
           for example, than in tall grass. Such situations shall be explicitly stated in the project
           specifications.
        6. It is commonly accepted that vertical accuracy testing in very irregular or steep
           sloping terrain is inappropriate due to the high probability that the error in the testing
           process is a significant contributor to the final error statistic and thus biases the
           results. For example a small but acceptable horizontal shift in the data may reflect in
           an unacceptable vertical error measurement. Because of this concern, ASPRS
           recommends that vertical accuracy testing always be done in areas where the terrain
           is as level and consistent as possible. In mountainous areas, level areas may not be
           easy to access, but attempts should be made to keep test points in reasonably low
           slope and smooth terrain as possible.

    Note that for the specific case of contour mapping, ASPRS does not support extrapolating a
    fundamental vertical accuracy across different land cover classes with the assumption the
    vertical accuracy will meet the stated mapping standard. For example, if a dataset is reported
    with a fundamental vertical accuracy that just meets the vertical accuracy requirement listed
    in Table 1 for the desired contour interval, it is probable that it will not meet that mapping
    standard outside of open terrain. Supplemental vertical accuracy reporting shall always be
    requested and provided for every land cover class for which it is intend to generate contour
    maps and care should be taken to verify that the required vertical accuracy for the given
    contour interval is met in each and every land cover class.

    For legacy datasets for which only a “vertical accuracy” was reported with no indication if
    this is fundamental, supplemental or consolidated accuracy, ASPRS recommends assuming
    this is a fundamental (best-case) vertical accuracy and recommends caution when working


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    with the dataset in different land cover classes. If possible, review the QA/QC data and re-test
    the data to measure supplemental vertical accuracies (95th percentile testing) in areas outside
    open terrain.

    1.2. Horizontal Accuracy
    Horizontal accuracy is another important characteristic of elevation data; however, it is
    largely controlled by the vertical accuracy requirement. If a very high vertical accuracy is
    required then it will be essential for the data producer to maintain a very high horizontal
    accuracy. This is because horizontal errors in elevation data normally, but not always,
    contribute significantly to the error detected in vertical accuracy tests.

    As a general rule, horizontal error is more difficult than vertical error to assess in lidar
    datasets. This is because the land surface often lacks distinct (well defined) topographic
    features necessary for such tests or because the resolution of the elevation data is too coarse
    for precisely locating distinct surface features. For these reasons, ASPRS does not require
    horizontal accuracy testing of lidar-derived elevation products. Instead, ASPRS requires data
    producers to report the expected horizontal accuracy of elevation products as determined
    from system studies or other methods. See ASPRS Guidelines: Horizontal Accuracy
    Reporting for Lidar Data (to be published) and ASPRS Guidelines: Sensor Calibration and
    Reporting (to be published) as well as section 1.5.3.4 of the NDEP Guidelines for further
    information on testing and reporting of the horizontal accuracy of lidar data.

    However, when considering vertical accuracy, it is important to specify some minimum
    expectation of horizontal accuracy for elevation data acquired using lidar, so ASPRS
    recommends Table 2 shall be used as a guideline. Note that a contractual horizontal accuracy
    specification for lidar data collection still requires the lidar data producer to ensure that an
    appropriate methodology and horizontal control structure is applied during the collection and
    processing of the elevation data and acceptable reporting procedures identified and agreed to
    by the contractor.

                NMAS                    NMAS                     NSSDA                           NSSDA
               Map Scale               CMAS 90%                  RMSE(r)                     Accuracy(r) 95%
                                                                                             confidence level

     1" = 100' or 1:1,200              3.33 ft           2.20 ft or 67.0 cm              3.80 ft or 1.159 m
     1" = 200' or 1:2,400              6.67 ft           4.39 ft or 1.339 m              7.60 ft or 2.318 m
     1" = 400' or 1:4,800              13.33 ft          8.79 ft or 2.678 m              15.21 ft or 4.635 m
     1" = 500' or 1:6,000              16.67 ft          10.98 ft or 3.348 m             19.01 ft or 5.794 m
     1" = 1000' or 1:12,000            33.33 ft          21.97 ft or 6.695 m             38.02 ft or 11.588 m
     1" = 2000' or 1:24,000 *          40.00 ft          26.36 ft or 8.035 m            45.62 ft or 13.906 m

                   Table 2 Comparison of NMAS/NSSDA Horizontal Accuracy

    * The 1:24,000- and 1:25,000-scales of USGS 7.5-minute quadrangles are smaller than 1:20,000; therefore, the
    NMAS horizontal accuracy test for well-defined test points is based on 1/50 inch, rather than 1/30 inch for maps
    with scales larger than 1:20,000.




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2. Accuracy Assessment and Reporting

    2.1. General Guidance
    The NSSDA specifies that vertical accuracy should be reported at the 95 percent confidence
    level for data tested by an independent source of higher accuracy as:

    “Tested __ (meters, feet) vertical accuracy at 95 percent confidence level.”

    For ASPRS purposes, the independent source of higher accuracy should be at least three
    times more accurate than the dataset being tested, whenever possible. The NSSDA further
    states that an alternative "Compiled to Meet" statement shall be used when the guidelines for
    testing by an independent source of higher accuracy cannot be followed and an alternative
    means is used to evaluate accuracy. Accuracy should be reported at the 95th percent
    confidence level for data produced according to procedures that have been consistently
    demonstrated to achieve particular vertical accuracy values as:

    “Compiled to meet __ (meters, feet) vertical accuracy at 95 percent confidence level.”

    For ASPRS purposes, the "Compiled to Meet" statement should be used by data producers
    when no independent test results are available or can be practically obtained. For example,
    vertical accuracy may be impossible to test against an independent source of higher accuracy
    in very remote or rugged terrain.

    It is important to note that the present NSSDA test for vertical accuracy is valid only if errors
    for the dataset follow a normal or Gaussian distribution, i.e., one defined by a bell-shaped
    curve. NSSDA modifications for testing and reporting accuracy of non-normal error
    distributions are being recommended to the FGDC by the NDEP. Whereas vertical errors in
    open terrain typically have a normal distribution, vertical errors do not typically follow a
    normal distribution in other land cover categories, especially in dense vegetation where even
    active sensors such as lidar may be unable to detect the ground. For this reason, additional
    ASPRS guidelines are provided below for reporting the vertical accuracy of lidar-derived
    elevation data in land cover categories other than open terrain. For example, forested areas,
    scrub, wheat or corn fields, tall weeds, mangrove, sawgrass, or urban terrain.

    2.2. Designing Accuracy Tests
    The NSSDA specifies:

        If data of varying accuracies can be identified separately in a dataset, compute and
        report separate accuracy values.

    Many factors will vary over time and space for any particular elevation production project.
    Major variations in certain factors may have significant influence on the resulting accuracy of
    the data. To derive an accuracy statistic that is meaningful and representative of the data,
    potential variables, such as those discussed below, should be considered during the design of
    the accuracy tests.

        2.2.1. Continuity of Data Collection and Processing
        Data producers have unique systems and procedures for collecting and processing lidar
        data. Any time multiple producers and collection systems are utilized to gather
        lidar data over the same project area, the data should be tested separately for each
        producer or collection system. System components (equipment, procedures, software,


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        etc.) may also vary over the life of a project. When there is reason to suspect that such
        changes may have a significant effect on accuracy, these variations should be tested
        separately.

        2.2.2. Topographic Variation
        Varying types of topography (such as mountainous, rolling, or flat terrain) within a
        project may affect the accuracy at which the elevation surface can be modeled. Also, for
        many applications, the accuracy requirement in high-relief terrain may be less than that
        for flat terrain. In such situations, it may be preferable to specify different accuracy
        requirements for the various terrain types and to design separate tests for each.

        2.2.3. Ground Cover Variation
        Studies have shown lidar errors to be significantly affected by various ground cover
        types. Because vegetation can limit ground detection, tall dense forests and even tall
        grass tend to cause greater elevation errors than unobstructed (short grass or barren)
        terrain. Errors measured in areas of different ground cover also tend to be distributed
        differently from errors in unobstructed terrain. For these reasons, ASPRS requires open
        terrain to be tested separately from other ground cover types. Testing over any other
        ground cover category is required only if that category constitutes a significant portion of
        the project area deemed critical to the customer.

    2.3. Selecting and Collecting Checkpoints
    ASPRS recommends that all checkpoint survey work to be used in verifying the vertical
    accuracy meets contractual specifications (as opposed to checkpoint data used by the lidar
    data provider for their own internal accuracy assessment tests) be undertaken by, or be under
    the supervision of, an independent survey firm licensed in the particular state where the
    project area is located. Independent in this case is taken to mean having no contractual or
    financial connections to the lidar data provider; in particular the survey firm should not have
    a subcontractor relationship to the data provider.

    Checkpoints should be well distributed throughout the dataset. ASPRS recommends the
    following NSSDA guidance be followed when choosing checkpoint locations:

        Checkpoints may be distributed more densely in the vicinity of important features and
        more sparsely in areas that are of little or no interest. When the distribution of error is
        likely to be nonrandom, it may be desirable to locate checkpoints to correspond to the
        error distribution. For a dataset covering a rectangular area that is believed to have
        uniform positional accuracy, checkpoints may be distributed so that points are spaced at
        intervals of at least 10 percent of the diagonal distance across the dataset and at least 20
        percent of the points are located in each quadrant of the dataset.

        2.3.1. Land Cover Categories
        The NSSDA states:

                A minimum of 20 checkpoints shall be tested, distributed to reflect the
                geographic area of interest and the distribution of error in the dataset. When 20
                points are tested, the 95 percent confidence level allows one point to fail the
                threshold given in product specifications.

        However, ASPRS recommends collecting a minimum of 20 checkpoints (30 is preferred)
        in each of the major land cover categories representative of the area for which lidar data


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         vertical accuracy is to be verified. This provides more robust characterization of the error
         distribution across the dataset and helps to identify potential systematic errors. Thus if
         five major land cover categories are determined to be applicable for a particular project,
         then a minimum of 100 total checkpoints are required. Note that in cases where more
         than 20 checkpoints are collected in a particular land cover class, vertical accuracy
         reporting is to be based on the 20 (or 30 preferred) worst or least accurate checkpoints in
         that land cover class, after eliminating checkpoints that have been identified as containing
         errors and blunders in the ground survey. It is not acceptable practice to collect an
         abundance of checkpoints and retain only the best for vertical accuracy reporting.

         The most common land cover categories are as follows:

                        !   Open terrain (sand, rock, dirt, plowed fields, lawns, golf courses).
                        !   Tall weeds and crops.
                        !   Brush lands and low trees.
                        !   Forested areas fully covered by trees.
                        !   Urban areas with dense man-made structures.

         It is up to the lidar data producer and customer to determine the significant land cover
         categories to be tested. The selection and definition of land cover categories should be
         based on the unique mix and variations of land cover for the project site and the potential
         effect of each on the surface application. Care should be taken to ensure adequate
         planning and QA/QC control is in place for each land cover class when derivative
         products, such as contour maps, are to be generated across an area with several different
         land cover classes. For some applications, distinction between grass, brush, and forest
         may not be sufficient. For example, where very high vertical accuracy is a must, it may
         be important to understand how variations in grass height and density affect the final
         vertical accuracy. In such situations, it may be preferable to break “grasses” into two or
         more categories based on species or stand characteristics.

         Whether land cover categories are user defined or chosen based on existing land cover
         categories such as the Anderson2 or National Land Cover Dataset3 land-use and land-
         cover classification systems, they need to be reported in the metadata. User defined
         categories should be simple, descriptive and representative of existing major land cover
         categories. For example, there is no Anderson Level II for lawns, but there is (11)
         residential, (16) mixed urban or built-up land, and (17) other urban or built-up land.
         There is a category for pasture, it is (21) cropland and pasture, but cropland normally has
         taller vegetation than "open terrain."

         2.3.2. Checkpoints
         The QC (quality control) checkpoints should be selected on flat terrain, or on uniformly
         sloping terrain for x-meters in all directions from each checkpoint, where "x" is the
         nominal spacing of the DEM or mass points evaluated. Whereas flat terrain is preferable,
         this is not always possible. Whenever possible, terrain slope should not be steeper than a
         20 percent grade because horizontal errors will unduly influence the vertical RMSE
         calculations. For example, an allowable 1-meter horizontal error in a DEM could cause
2
  For a detailed description of this system, see USGS Professional Paper 964, A Land Use and Land Cover
Classification System for Use with Remote Sensor Data. This system is commonly referred to as the "Anderson
Classification".
3
 The NLCD 1992 Classification System is available online at http://www.epa.gov/mrlc/definitions.html.




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        an apparent unallowable vertical error of 20 cm in the DEM. Furthermore, checkpoints
        should never be selected near severe breaks in slope, such as bridge abutments or edges
        of roads, where subsequent interpolation might be performed with inappropriate TIN or
        DEM points on the wrong sides of the break lines.

        Checkpoint surveys should be performed relative to National Spatial Reference System
        (NSRS) monuments of high vertical accuracy, preferably using the very same NSRS
        monuments used as GPS base stations for airborne GPS control of the mapping aircraft.
        This negates the potential that elevation differences might be attributed to inconsistent
        survey control.

        To extend control from the selected NSRS monuments into the project area, it is
        recommended that NOAA Technical Memorandum NOS NGS-58, "Guidelines for
        Establishing GPS-Derived Ellipsoid Heights (Standards: 2 cm and 5 cm)," November,
        1997 (NOAA, 1997) be used, using the National Geodetic Survey's latest geoid model to
        convert from ellipsoid heights to orthometric heights. GPS real-time-kinematic (RTK)
        procedures are acceptable as long as temporary benchmarks within the project area are
        surveyed twice with distinctly different satellite geometry to overcome the possibility of
        GPS multipath error. Subsequent to GPS surveys to extend control into the project area,
        conventional third-order surveys can be used to extend control to checkpoints that are
        typically located within forested areas or "urban canyons" where GPS signals would be
        blocked. QC surveys should be such that the checkpoint accuracy is at least three times
        more accurate than the dataset being evaluated. For example, if a DEM is supposed to
        have a vertical RMSE(z) of 18.5-cm, equivalent to the accuracy required of 2' contours,
        then the checkpoints should be surveyed with procedures that would yield vertical
        RMSE(z) of 6.0 cm or better.

        In all methods of accuracy testing and reporting, there is a presumption that the
        checkpoint surveys are error free and that discrepancies are attributable to the lidar
        technology assumed to have lower accuracy. This is especially true when the checkpoint
        surveys are performed with technology and procedures that should yield accuracies at
        least three times greater than the expected accuracy of the remote sensing data being
        tested. However, checkpoint surveys are not always error free, and care must be taken to
        ensure that all survey errors and blunders are identified. When discrepancies do appear,
        resurveying questionable checkpoints themselves, or asking for the original checkpoint
        survey data to be reviewed are ways to challenge the accuracy, or inaccuracy, of the
        checkpoints. Because of potential challenges to the surveyed checkpoints, it is
        recommended that each checkpoint be marked with a recoverable item, such as a 60d nail
        and an adjoining flagged stake, to assist in recovery of the checkpoints for resurveys.

    2.4. Deriving Dataset Elevations for Checkpoints
    Once checkpoints are collected and checked for blunders, elevations corresponding to each
    checkpoint must be derived from each lidar dataset to be tested. Exact procedures for
    obtaining these elevations will vary depending on the elevation data model and on software
    tools available for the test.

    Whereas checkpoints may be considered to be well-defined and recoverable, mass points,
    TIN/DEM points, and contours are not. Because digital elevation models derived from lidar
    data do not contain well-defined points, it is difficult to test exactly the same points measured
    as checkpoints in the lidar-derived DEM or TIN dataset. Therefore, it is usually necessary to



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       interpolate an elevation from the surface model at the horizontal (xy) location of each
       checkpoint.

            2.4.1. TIN Interpolation
            When mass points are specified as a deliverable, a TIN derived from the mass points
            provides a surface from which elevations can be directly interpolated at the horizontal
            location of each checkpoint. A number of commercial software packages have
            commands4 that perform this interpolation automatically for a list of checkpoints.

            2.4.2. DEM Interpolation
            When a gridded DEM is specified as a deliverable, it must be tested to ensure it meets
            required accuracies even when a TIN with a “Tested to Meet” accuracy statement is used
            as the DEM source. This is because generalization or smoothing processes employed
            during DEM interpolation may degrade the elevation surface. If a gridded DEM is to be
            tested, surface elevations at the checkpoint locations can be interpolated using a suitable
            interpolation scheme. 5

            2.4.3. Contour Interpolation
            Contours may be directly collected from stereoscopic source by a compiler or may be
            generated from a lidar-derived TIN or DEM. The contours should be tested when
            specified as a deliverable whether they were directly compiled or derived from another
            data model, even if the source model meets required accuracies. This is because the
            accuracy of any derived product can be degraded by interpolation, generalization, or
            smoothing. Contour tests can be performed two ways. One method consists of plotting
            checkpoint locations in relationship with surrounding contours and mentally interpolating
            an elevation for that checkpoint from surrounding contours. Another method requires the
            contours to be converted to a TIN, from which elevations can be automatically
            interpreted with software. The TIN method is somewhat risky because TINing software
            cannot apply the rationale that may be required of the human during interpolation.
            Therefore, the TINing process may introduce additional error into the interpolated
            elevations. However, if the TIN test meets accuracy, one can be fairly confident that the
            contours meet accuracy. If the TIN accuracy fails, it may be necessary to perform the
            mental interpolation and retest.

            2.4.4. Direct Measurement
            It should be noted that a direct test of the accuracy of the elevation data may be
            performed by conducting field measurements after the locations of the unique lidar
            returns are known. By surveying checkpoints on the known xy coordinates of ground
            surface lidar point data, a direct comparison can be used as a means of verifying vertical
            accuracy, removing the introduction of errors caused by interpolating the elevation value
            from a TIN, a DEM or contour interpolation. Given that most elevation data will be used
            to generate additional mapping products through TINing, DEM generation, or contour
            maps, ASPRS does not recommend this procedure as a final QC procedure for reporting
            the vertical accuracy of datasets. When direct measurements are used to calculate the
            vertical accuracy of the dataset, this fact must be clearly reported along with a caution
            about the potential of introducing further interpolation error in any derived mapping
            products.

4
    For example, Arc/Info TINSPOT.
5
    For example a 4-neighbor bilinear interpolation such as that used in the ArcInfo Latticespot command.




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    2.5. Computing Errors
    The "difference" or error for each checkpoint is computed by subtracting the surveyed
    elevation of the checkpoint from the lidar dataset elevation interpolated at the x/y coordinate
    of the checkpoint. Thus, if the difference or error is a positive number, the evaluated dataset
    elevation is higher than true ground in the vicinity of the checkpoint, and if the difference is a
    negative number, the evaluated dataset elevation is lower.

        For Checkpoint(i), the Vertical Error(i) = (Zdata(i) – Zcheck(i))

        Where:
                 Zdata(i) is the vertical coordinate of the ith checkpoint in the dataset
                 Zcheck(i) is the vertical coordinate of the ith checkpoint in the independent
                 source of higher accuracy
                 i is an integer from 1 to n; n = the number of points being checked

    2.6. Analyzing Errors

        2.6.1. Blunders, Systematic Error, and Random Error
        The "errors" measured in accuracy calculations, in theory, pertain only to random errors,
        produced by irregular causes whose effects upon individual observations are governed by
        no known law that connects them with circumstances and so cannot be corrected by use
        of standardized adjustments. Random errors typically follow a normal distribution.
        Systematic errors follow some fixed pattern and are introduced by data collection
        procedures and systems. Systematic errors may occur as vertical elevation shifts across a
        portion or all of a dataset. These can be identified through spatial analysis of error
        magnitude and direction or by analyzing the mean error for the dataset. Systematic errors
        may also be identified as large deviations from the true elevations caused by
        misinterpretations of terrain surfaces due to trees, buildings, and shadows, fictitious
        ridges, tops, benches, and striations. A systematic error is predictable in theory and is,
        therefore, not random. Where possible, systematic errors should be identified and
        eliminated from a set of observations prior to accuracy calculations.

        A blunder is an error of major proportion, normally identified and removed during editing
        or QC processing. A potential blunder may be identified as any error greater than three
        times the standard deviation (3 sigma) of the error. Errors greater than 3 sigma should be
        analyzed to determine the source of the blunder and to ensure that the blunder is not
        indicative of some unacceptable source of systematic error. Checkpoints with large error
        should not simply be thrown out of the test sample without investigation; they may
        actually be representative of some error characteristic remaining in the elevation surface
        and should be addressed in the metadata.

        It is generally accepted that errors in open terrain represent random errors in the lidar
        sensor system, whereas errors in vegetated areas may include systematic errors. For
        example, systematic inability to penetrate dense vegetation, and/or systematic
        deficiencies in procedures used to generate bare-earth elevation datasets. A single large
        error (outlier) in a forested area, for example, can totally skew RMSE calculations of a
        large population of checkpoints that otherwise satisfy the accuracy criteria.



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3. Calculating and Reporting Vertical Accuracy – ASPRS Requirements

    3.1. Fundamental Vertical Accuracy
    The fundamental vertical accuracy of a dataset must be determined with checkpoints
    located only in open terrain, where there is a very high probability that the sensor will have
    detected the ground surface. The fundamental accuracy is the value by which vertical
    accuracy can be equitably assessed and compared among different datasets. Fundamental
    accuracy is calculated at the 95-percent confidence level as a function of RMSE(z).

    3.2. Supplemental and Consolidated Vertical Accuracies
    In addition to the fundamental accuracy, supplemental or consolidated accuracy values
    may be calculated for other ground cover categories or for combinations of ground cover
    categories respectively. Because elevation errors often vary with the height and density of
    ground cover, a normal distribution of error cannot be assumed and, therefore, RMSE(z)
    cannot be used to calculate the 95-percent accuracy value. Consequently a nonparametric
    testing method (95th Percentile) is required for supplemental and consolidated accuracy tests.

    95th Percentile Error
    For supplemental and consolidated accuracy tests, the 95th percentile method shall be
    employed to determine accuracy. The 95th percentile method may be used regardless of
    whether or not the errors follow a normal distribution and whether or not errors qualify as
    outliers. Computed by a simple spreadsheet command, a "percentile" is the interpolated
    absolute value in a dataset of errors dividing the distribution of the individual errors in the
    dataset into one hundred groups of equal frequency. The 95th percentile indicates that 95
    percent of the errors in the dataset will have absolute values of equal or lesser value and 5
    percent of the errors will be of larger value. With this method, Accuracy(z) is directly equated
    to the 95th percentile, where 95 percent of the errors have absolute values that are equal to or
    smaller than the specified amount.

    Prior to calculating the data accuracy, these steps should be taken:

        ! Separate checkpoint datasets according to important variations in expected error such
          as by land cover class (see for example NDEP Guidelines section 1.5.2.2).
        ! Edit collected checkpoints to identify, remove or minimize errors and blunders (see
          for example NDEP Guidelines section 1.5.2.3).
        ! Interpolate the elevation surface for each checkpoint location (see for example NDEP
          Guidelines section 1.5.2.4)
        ! Identify and eliminate lidar sensor systematic errors and/or blunders in the lidar data
          processing (see for example NDEP Guidelines sections 1.5.2.5 and 1.5.2.6).

    Once these steps are completed, the fundamental vertical accuracy must be calculated. If
    additional land cover categories are to be tested, supplemental and/or consolidated accuracies
    may also be computed.

    Fundamental Vertical Accuracy Test
    Using checkpoints in open terrain only:

        1. Compute RMSE(z) = Sqrt[(Σ(Zdata(i) – Zcheck(i)) 2 )/n]




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        2. Compute Accuracy(z) = 1.9600 * RMSE(z) = Vertical Accuracy at 95 percent
           confidence level.
        3. Report Accuracy(z) as:
            “Tested ______(meters, feet) fundamental vertical accuracy at 95 percent
            confidence level in open terrain using RMSE(z) x 1.9600.”


    Supplemental Vertical Accuracy Tests
    The following accuracy tests are considered optional, except in cases where the mapping
    products being generated require specific vertical accuracies be met by each land cover class
    (e.g. contour mapping). When used, these tests must be accompanied by fundamental vertical
    accuracy tests. The only possible exception to this rule is the rare situation where accessible
    pockets of open terrain (road clearings, stream beds, meadows, or isolated areas of exposed
    earth) do not exist in sufficient quantity for collecting the minimum test points. Only in this
    instance may supplemental or consolidated accuracies be reported without an accompanying
    fundamental accuracy. However, this situation must be explained in the metadata. Most
    likely, when producing an elevation surface where little or no accessible open-terrain exists,
    the data producer will employ a collection system that has been previously tested to meet
    certain accuracies and a “Compiled to Meet” statement would be used in lieu of a “Tested to
    Meet” statement.

    When testing ground cover categories or combinations of categories excluding open terrain:

        1. Compute 95th percentile error (described above) for each category (or combination of
           categories).
        2. Report:
            “Tested ______(meters, feet) supplemental vertical accuracy at 95th percentile
            in (specify land cover category or categories)”
        3. In the metadata, document the errors larger than the 95th percentile. For a small
           number of errors above the 95th percentile, report x/y coordinates and z-error for
           each QC checkpoint error larger than the 95th percentile. For a large number of
           errors above the 95th percentile, report only the quantity and range of values.

    Consolidated Vertical Accuracy Tests
    When 40 or more checkpoints are consolidated for two or more of the major land cover
    categories, representing both the open terrain and other land cover categories (for example,
    forested), a consolidated vertical accuracy assessment may be reported as follows:

        1. Compute 95th percentile error (described above) for open terrain and other categories
           combined.
        2. Report
            “Tested ______(meters, feet) consolidated vertical accuracy at 95th percentile
            in: open terrain, (specify all other categories tested)”
        3. In the metadata, document the errors larger than the 95th percentile. For a small
           number of errors above the 95th percentile, report x/y coordinates and z-error for
           each QC checkpoint error larger than the 95th percentile. For a large number of errors
           above the 95th percentile, report only the quantity and range of values.


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    Failed Accuracy Tests
    If the fundamental vertical accuracy test fails to meet the prescribed accuracy, there is a
    serious problem with the control, collection system, or processing system or the achievable
    accuracy of the production system has been overstated. If a systematic problem can be
    identified, it should be corrected, if possible, and the data should be retested. If a systematic
    problem cannot be identified, it is probable that the entire dataset will need to be recollected,
    depending on the contractual agreement with the data provider.

    If a dataset passes the fundamental vertical accuracy test, but fails to meet supplemental or
    consolidated vertical accuracy tests (e.g. meets prescribed accuracy in open terrain, but not in
    forested areas), there may be a problem with the control, collection system, or processing
    system as above. It is also possible that the data was collected with equipment, procedures or
    methods designed to just meet the fundamental vertical accuracy requirement in open terrain,
    but that fail to take in to account the degradation of accuracy in other land cover classes.
    However, a more probable explanation is that serious errors may have occurred in automated
    or manual filtering of the lidar data. If such errors can be identified, they should be corrected,
    if possible, and the data should be retested. If such errors cannot be identified, the areas
    impacted may need to be excluded from the dataset or data recollected for the affected areas,
    depending on the contractual agreement with the data provider.

    3.3. Reporting Vertical Accuracy of Untested Data – ASPRS Requirements
    Use the ‘Compiled to Meet’ statement below when the above guidelines for testing by an
    independent source of higher accuracy cannot be followed and an alternative means is used to
    evaluate accuracy. Report accuracy at the 95th percent confidence level for data produced
    according to procedures that have been demonstrated to produce data with particular vertical
    accuracy values as:

    “Compiled to meet ___ (meters, feet) fundamental vertical accuracy at 95 percent
    confidence level in open terrain.”

    The following accuracy statements are optional. When used they must be accompanied by a
    fundamental vertical accuracy statement. For ground cover categories other than open
    terrain, report:

    “Compiled to meet ___ (meters, feet) supplemental vertical accuracy at 95th percentile in
    (specify land cover category or categories).”

    For all land cover categories combined, report:

    “Compiled to meet ___ (meters, feet) consolidated vertical accuracy at 95th percentile in:
    open terrain, (list all other relevant categories).”

    3.4. Testing and Reporting Horizontal Accuracy – ASPRS Requirements
    ASPRS does not require independent testing of horizontal accuracy for lidar-derived
    elevation products. Instead, ASPRS requires data producers to report the expected horizontal
    accuracy of elevation products as determined from system studies or other methods. See
    ASPRS Lidar Guidelines: Horizontal Accuracy Reporting for Lidar Data (to be published)
    and ASPRS Lidar Guidelines: Sensor Calibration and Reporting (to be published) as well as
    section 1.5.3.4 of the NDEP Guidelines for further information on testing and reporting of the
    horizontal accuracy of lidar data.


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    3.5. Accuracy Assessment Summary
    Providers of lidar elevation data use a variety of methods to control the accuracy of their
    products. Lidar data providers may collect hundreds of static or kinematic control points for
    internal quality control and to adjust their datasets to these control points. To the degree that
    such control points are used in a fashion similar to control for aerotriangulation in
    photogrammetry, by which the datasets are adjusted to better fit such control points, then
    lidar data providers may use the "Compiled to Meet" accuracy statements listed above for
    such datasets.

    Note, however, that with mature technologies such as photogrammetry, users generally
    accept "Compiled to Meet" accuracy statements without independent accuracy testing due to
    the rigorous methodology and recognized best practices that support such mature technology.
    However, with developing technologies such as lidar, users often require independent
    accuracy tests even for “Compiled to Meet” accuracy statements; testing for which, as
    outlined above, is more complex, especially when errors include "outliers" or do not follow a
    normal distribution as required for the use of RMSE in accuracy assessments. Because of
    these complexities, ASPRS strongly recommends the "truth in advertising" approach,
    whereby lidar data providers report vertical accuracies in open terrain separately from other
    land cover categories, report vertical accuracies in other than open terrain using 95th
    percentile testing and document the size of the errors larger than the 95th percentile in the
    metadata, regardless of the intention of the contractor to independently test (or not) such
    statements.

    3.6 Relative Vertical Accuracy
    The accuracy measurement discussed in these guidelines refers to absolute vertical accuracy,
    which accounts for all effects of systematic and random errors. For some applications of
    lidar elevation data, the point-to-point (or relative) vertical accuracy is more important than
    the absolute vertical accuracy. Relative vertical accuracy is controlled by the random errors
    in a dataset. The relative vertical accuracy of a dataset is especially important for derivative
    products that make use of the local differences among adjacent elevation values, such as
    slope and aspect calculations. Because relative vertical accuracy may be difficult to measure
    unless a very dense set of reference points is available, this ASPRS guideline does not
    prescribe an approach for its measurement. If a specific level of relative vertical accuracy is a
    stringent requirement for a given project, then the plan for collection of reference points for
    validation should account for that. Namely, reference points should be collected at the top
    and bottom of uniform slopes. In this case, one method of measuring the relative vertical
    accuracy is to compare the difference between the elevations at the top and bottom of the
    slope as represented in the elevation model vs. the true surface (from the reference points). In
    many cases, the relative vertical accuracy will be much better than the absolute vertical
    accuracy, thus the importance of thoroughly measuring and reporting the absolute accuracy,
    as described in these guidelines, so the data users can have an idea of what relative accuracy
    to expect.




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    GLOSSARY:

    Accuracy – the closeness of an estimated (for example, measured or computed) value to a
    standard or accepted [true] value of a particular quantity. Note: Because the true value is not
    known, but only estimated, the accuracy of the measured quantity is also unknown.
    Therefore, accuracy of coordinate information can only be estimated.

        • Absolute Vertical Accuracy – a measure that relates the stated elevation to the true
        elevation with respect to an established vertical datum. The computed value for the
        absolute vertical accuracy (tested, or compiled to) should be included in the metadata file.

    Artifacts – Buildings, trees, towers, telephone poles or other elevated features that should be
    removed when depicting a DEM of the bare-earth terrain. Artifacts are not just limited to real
    features that need to be removed. They also include unintentional byproducts of the
    production process, such as stripes in manually profiled DEMs. Any feature, whether man-
    made or system-made, that unintentionally exists in a digital elevation model.

    ASPRS - American Society for Photogrammetry and Remote Sensing

    Calibration – Procedures used to identify systematic errors in hardware, software, and
    procedures so that these errors can be corrected in preparing the data derived there from.

    Checkpoint – One of the points in the sample used to estimate the positional accuracy of the
    dataset against an independent source of higher accuracy.

    Confidence level – The probability that errors are within a range of given values.

    Consolidated vertical accuracy – The result of a test of the accuracy of 40 or more check
    points (z-values) consolidated for two or more of the major land cover categories,
    representing both the open terrain and other land cover categories. Computed using a
    nonparametric testing method (95th Percentile), a consolidated vertical accuracy is always
    accompanied by a fundamental vertical accuracy. See fundamental and supplemental vertical
    accuracies.

    Contour – A line connecting points of equal elevation.

    Contour interval – The difference in z-values between contours.

    DEM - Digital Elevation Model - has at least three different meanings:

        • “DEM” is a generic term for digital topographic and/or bathymetric data in all its
        various forms. Unless specifically referenced as Digital Surface Models (DSMs), the
        generic DEM normally implies elevations of the terrain (bare earth z-values) void of
        vegetation and manmade features.

        • As used by the U.S. Geological Survey (USGS), a DEM is the digital cartographic
        representation of the elevation of the land at regularly spaced intervals in x and y
        directions, using z-values referenced to a common vertical datum. There are many types
        of standard USGS DEMs.




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        • As used by other users in the U.S. and elsewhere, a DEM has bare earth z-values at
        regularly spaced intervals in x and y, but normally following alternative specifications,
        with narrower grid spacing and State Plane coordinates for example.

    DTED - Digital Terrain Elevation Data – Standard elevation datasets of the National
    Geospatial-Intelligence Agency (NGA), similar to standard USGS DEMs described above.

    DTM - Digital Terrain Model - has at least two different definitions:

        • In some countries, DTMs are synonymous with DEMs, representing the bare earth
        terrain with uniformly spaced z-values.

        • As used herein, DTMs may be identical to DEMs, but they may also incorporate the
        elevation of significant topographic features on the land and change points and breaklines
        that are irregularly spaced so as to better characterize the true shape of the bare earth
        terrain. The net result of DTMs is that the distinctive terrain features are more clearly
        defined, and contours generated from DTMs more closely approximate the real shape of
        the terrain. Such DTMs are normally more expensive and time consuming to produce
        than uniformly spaced DEMs because breaklines are ill suited for automation; but the
        DTM results are technically superior to standard DEMs for many applications.

    DSM - Digital Surface Model - – Similar to DEMs or DTMs, except that they depict the
    elevations of the top surfaces of buildings, trees, towers, and other features elevated above the
    bare earth. DSMs are especially relevant for telecommunications management, forest
    management, air safety, 3-D modeling and simulation.

    Elevation – The distance measured upward along a plumb line between a point and the
    geoid. The elevation of a point is normally the same as its orthometric height, defined as
    “H” in the equation: H = h – N. This is the “official” geodesy definition of elevation, but the
    term elevation is also used more generally for height above a specific vertical reference, not
    always the geoid.

    FGDC - Federal Geographic Data Committee (FGDC) http://www.fgdc.gov/

    Fundamental vertical accuracy – The fundamental vertical accuracy is the value by which
    vertical accuracy can be equitably assessed and compared among datasets. The fundamental
    vertical accuracy of a dataset must be determined with check points located only in open
    terrain where there is a very high probability that the sensor will have detected the ground
    surface. It is obtained utilizing standard tests for RMSE. See supplemental and consolidated
    vertical accuracies.

    Grid – A geographic data model that represents information as an array of equally sized
    square cells. Each grid cell is referenced by its geographic or x/y orthogonal coordinates.

    Horizontal accuracy – Positional accuracy of a dataset with respect to a horizontal datum.

    Independent source of higher accuracy – Data acquired independently of procedures to
    generate the dataset that is used to test the positional accuracy of a dataset. The independent
    source of higher accuracy shall be of the highest accuracy feasible and practicable to evaluate
    the accuracy of the dataset.



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    Interpolation – The estimation of z-values at a point with xy coordinates, based on the
    known z-values of surrounding points.

    Lidar – Light Detection and Ranging – An instrument that measures distance to an object by
    emitting timed pulses of light and measuring the time between emission and reception of
    reflected pulses. The measured time interval is converted to a distance.

    Mass points – Irregularly spaced points, each with an xy location and a z-value, used to form
    a TIN. When generated manually, mass points are ideally chosen to depict the most
    significant variations in the slope or aspect of TIN triangles. However, when generated by
    automated methods, For example, by lidar, mass point spacing and pattern depend on
    characteristics of the technologies used to acquire the data. Mass points are most often used
    to make a TIN, but not always. They can be used as XYZ point data for interpolation of a grid
    without an intermediate TIN stage.

    NDEP - National Digital Elevation Program

    NSRS - National Spatial Reference System

    NSSDA - National Standard for Spatial Data Accuracy

    Post spacing – The z-values at regularly spaced intervals of a grid (the ground distance in x
    and y ("post spacing" = .x = .y)). The post spacing is usually specified in units of whole feet
    or meters. Actual grid spacing, datum, coordinate system, data format, and other
    characteristics may vary widely from grid to grid.

    Profile – A vertical view of a surface derived by sampling surface values along a specified
    line. In USGS DEMs, profiles are the basic building blocks of an elevation grid and are
    defined as one-dimensional arrays, i.e., arrays of n columns by 1 row, where n is the length of
    the profile.

    Relative Accuracy – A measure that accounts for random errors in a dataset. Relative
    accuracy may also be referred to as point-to-point accuracy. The general measure of relative
    accuracy is an evaluation of the random errors (systematic errors and blunders removed) in
    determining the positional orientation (For example, distance, azimuth, elevation) of one
    point or feature with respect to another.

    Relative Vertical Accuracy – A measure of the point-to-point vertical accuracy within a
    specific dataset. To determine relative vertical accuracy, the vertical difference between two
    points is measured. That difference is then compared to the difference in elevation for the
    same two points on the reference. The difference between the two measures represents the
    relative accuracy. The reference must have at least three times the accuracy of the intended
    product accuracy, insuring that all systematic errors and blunders have been removed.
    Relative vertical accuracy, an important characteristic of elevation data used for calculating
    slope, should be documented in the DEM metadata file.

    Resolution – In the context of gridded elevation data, resolution is related to the horizontal
    post spacing and the vertical precision. Other definitions include:

        • The size of the smallest feature that can be represented in a surface or image.



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        • Sometimes used to state the number of points in x and y directions in a lattice, for
        example, 1201 x 1201 mesh points in a USGS one-degree DEM

    Root mean square error – The square root of the mean of squared errors for a sample.

    Slope – The measure of change in z-value over distance, expressed either in degrees or as
    a percent. For example, a rise of 4 meters over a distance of 100 meters describes a 2.3°
    or 4 percent slope.

    Surface – a 3-D geographic feature represented by computer models built from uniformly- or
    nonuniformly-spaced points with x/y coordinates and z-values.

    Supplemental vertical accuracy – The result of a test of the accuracy of z-values over areas
    with ground cover categories or combinations of categories other than open terrain. Obtained
    utilizing the 95th percentile method, a supplemental vertical accuracy is always accompanied
    by a fundamental vertical accuracy. See fundamental and consolidated vertical accuracies.

    Triangulated Irregular Networks (TINs) – A set of adjacent, nonoverlapping triangles
    computed from irregularly spaced points with xy coordinates and z-values. The TIN data
    structure is based on irregularly spaced point, line, and polygon data interpreted as mass
    points and breaklines. The TIN model stores the topological relationship between triangles
    and their adjacent neighbors. The TIN data structure allows for the efficient generation of
    surface models for the analysis and display of terrain and other types of surfaces. TINs
    usually require fewer data points than DEMs or DTMs, while capturing critical points that
    define terrain discontinuities and are topologically encoded so that adjacency and proximity
    analyses can be performed.

    Vertical accuracy – Measure of the positional accuracy of a dataset with respect to a
    specified vertical datum.

    Vertical error – The displacement of a feature’s recorded elevation in a dataset from its true
    or more accurate elevation.




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    Appendix A: Cross-Reference to NDEP Guidelines for Elevation Data (V1.0)

                    ASPRS Guidelines Section Number                             Corresponding NDEP Guidelines Section Number
     1.1. Vertical Accuracy                                              1.5.1.1 Vertical Accuracy
     1.2. Horizontal Accuracy                                            1.5.1.2 Horizontal Accuracy
     2.0 Accuracy Assessment and Reporting                               1.5.2 Accuracy Assessment
     2.1 General Guidance                                                1.5.2.1 General Guidance
     2.2 Designing Accuracy Tests                                        1.5.2.2 Designing Accuracy Tests
     2.3 Selecting and Collecting Checkpoints                            1.5.2.3 Selecting & Collecting Checkpoints
     2.4 Deriving Dataset Elevations for Checkpoints                     1.5.2.4 Deriving Dataset Elevations for Checkpoints
     2.5 Computing Errors                                                1.5.2.5 Computing Errors
     2.6 Analyzing Errors                                                1.5.2.6 Analyzing Errors
     3.0 Calculating & Reporting Vertical Accuracy                       1.5.3 Calculating and Reporting Vertical Accuracy
     3.1 Fundamental Vertical Accuracy                                   1.5.3.1 Fundamental Accuracy
     3.2 Supplemental and Consolidated Vertical Accuracies               1.5.3.2 Supplemental and Consolidated Vertical Accuracies
     3.3 Reporting Vertical Accuracy of Untested Data                    1.5.3.3 Reporting Vertical Accuracy of Untested Data
     3.4 Testing and Reporting Horizontal Accuracy                       1.5.3.4 Testing and Reporting Horizontal Accuracy
     3.5 Accuracy Assessment Summary                                     1.5.3.5 Accuracy Assessment Summary
     3.6 Relative Vertical Accuracy                                      1.5.3.6 Relative Vertical Accuracy




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